Since I was a child, I have a had a strong connection with nature, and I remember always admiring its beauty. I’ve read articles about the Earth being polluted making it a harmful place to live. I’ve tried to find ways to help the earth such as reusing water bottles, recycling as much as possible, going to local cleanups, and even planting native plants to help preserve the ecosystem. Once I reached high school, I was thrilled to join the environmental club knowing that I will be able to help the Earth at a larger scale with closest friends. I’m currently a part of the board of the club joyfully finding ways to help preserve the planet at a larger scale. However, it takes more than a few people to clean up everyone else’s mess. The amount of pollution dumped on our planet is a global issue that requires many knowledgeable people to help. When researching about mathematics in nature, I came upon the idea of how large of an effect the U.S., the most powerful first world country, has on the amount of waste dumped into the ocean. I chose to do my IA on the amount of waste produced by the United States because it will be a way to reflect on the country’s carbon footprint along with my effect as a person on Earth. My aim is to calculate the amount of municipal solid waste generated by the United States, how much of that waste is released into the ocean, and how much of the waste is recycled. Earth is the home to many unique species and home to billions of humans that plan on being around for a long time, so it is important to keep the Earth a safe home for future generations. Humans have been known to want the next big thing and then do away with anything that they can’t use anymore. The amount of municipal solid waste produced by people around the world has been rapidly increasing. According to the Word Bank, municipal solid waste is “non hazardous waste generated in households, commercial and business establishments, institutions, and non-hazardous industrial process wastes, agricultural wastes and sewage sludge. In practice, specific definitions vary across jurisdictions.” Following the years of industrialization dating back to the late 1700s to the early 1800s, humans have been able to produce and consume more than ever. Where does it all end up? After we throw away our waste in the trashcan it will usually end up in one of two places- landfills or as pollution in our oceans, a home to a vast amount of unique creatures. In my IA, I will be calculating the amount of municipal solid waste generated by the U.S. since 1960 to reflect on how much trash will be generated in future years. I will also be calculating how much of the waste was recycled, and I calculate how much of the trash produced by the United States covers the ocean. Based on data previously collected by the EPA, I will be formulating a function to reflect on the amount of trash generated by the U.S.The amount of municipal solid waste produced by the U.S. from 1960-2010X (years that have passed since 1960)Y (amount of MSW in million tons)1960 (0)88.11965 (5)104.41970 (10)121.11975 (15)127.81980 (20)151.61985 (25)166.31990 (30)208.31995 (35) 217.32000 (40)243.52005 (45)253.72010 (50)250.4As a result of this data, I found a common geometric sequence in the data that I can use  create a function. Un=U1rn-1f(x)= a rxI converted the original equation so it will fit the data by replacing U1 as a for my first term and rxas the difference between the sequence.f(0)= a r0=88.1After plugging in 0, considering 1960 was the first year the data was collected, to the equation the requals to 1.a=88.1My first term, a, in the geometric sequence is 88.1 million tons of waste. f(x)= 88.1 rxf(5)= 88.1 r5= 104.4r5=104.488.1= 1.185017026r51/5=(1.185017026)1/5r1.034534357The rate of garbage disposed by Americans from 1960-2010 per year was about 1.03 million tons. To find my difference in the geometric sequence, I plugged in 5 to x which is the difference between the years the amount of trash dumped was collected. I solved for r to give me the difference between the amount of trash between the 5 year intervals.f(x)= 88.1 1.03xThis equation demonstrates the geometric sequence based on the data. Keep in mind the equation does not take into consideration that there was a change in population affecting the amount of MSW, so the equation is theoretical.  Using this function, I will be able to estimate the amount MSW that was and will be  generated by the United States from 2015-2050. Once again, this equation will be used without taking into considreation any population growth that will occur between the years of 2015-2050. This would encourage an error in the math. f(55)= 88.1 1.0355I plugged in 55 because the difference between 2015- 1960 would 55 years that has passed.f(55)= 88.1 5.082148592I simplified 1.0355to multiply it by 88.1. I will not round until the end to prevent uncertainties. f(55) 447.7 million tons The amount of MSW generated by the U.S. in 2015 would be about 447.7 million tons. With this I will be able to find the projected amount of MSW generated by Americans until 2050. The projected amount of MSW produced the U.S. from 2015-2050X (years)Y (amount of MSW)2015 (55)447.72020 (60)519.12025 (65)601.72030 (70)697.12035 (75)808.72040 (80)937.52045 (85)1086.62050 (90)1259.9These numbers were calculated by plugging in the difference of years that have passed from 1960 to the year needed to find how much MSW was produced by the U.S. during  a span of 5 years.  The numbers are theoretical because the function does not take into consideration that the U.S. may use a renewable source of energy or lower on the amount of MSW used thus causing an error in the data. The graph is a visual representation of the data to prove that the projected amount of MSW produced by the U.S. from 2015 to 2050. From this, I believe Americans are producing far more garbage than what our land can hold. It’s important for us to understand that these numbers indicate that there will be an overwhelming amount of garbaged produced that Americans will not be able to get rid of and it can contaminate our enviornment ans even our drinking water. Moreover, in order to find the amount of MSW generated by the U.S. in 2017, it is important find the difference of years from 1960 to 2017 and plug that number into my x value. 2017-1960=57=xf(57)=88.1 1.0357f(57)= 88.1 5.391651441f(57)= 475.0 million tons Based on these calculations, Americans would have produced 475 million tons of municipal solid waste in the 2017 alone. This is is frightening idea knowing that my home country produces so many millions of tons of waste and we as a nation do not find shame for the amount of waste we produce. I think this is evidence that Americans should think twice about the materials they use, and hopefully we realise we can reuse most of our sources to make sure people are being resourceful and not dumping out so much stuff. I believe this is important statistic because such a high amount of trash was produced in only one year. Moreover, the EPA calculated that “34.5 percent” of the MSW generated by the United States is recycled. Based on the data collected by the EPA, there has been a continuous increase of MSW being recycled. In my opnion, this is a silver linning in America’s future because it shows that American’s understood the importance of keeping our home a safe and clean place for future generations. The amount of MSW recycled between 1960-2010 is shown in the table below.The amount of MSW recycled in the U.S. from 1960-2010X (years that have past since 1960)Y (amount of MSW recycled in million tons)1960 (0)5.61965 (5)6.51970 (10)8.01975 (15) 9.31980 (20)14.51985 (25)16.71990 (30)33.21995 (35)55.82000 (40)69.52005 (45) 79.82010 (50) 85.2There was no evidence of a geometric sequence in the data, but the data is still exponentially increasing. In order to come up with an equation that best fits the data, the best equation would be putting the data in the function f(x)=ax+b, where a and b are constants. Once the data was plugged into the GDC, the a= 2.13 and b=-19.8. The equation to demonstrate the data is: f(x)= 2.13x -19.8 This equation can also be used to predict the amount of MSW can will be recycled from 2015-2050. To find the amount of MSW that will be recycled, the difference from 1960 to the specific year the data was calculated with be put in place for x. This is similar to how I was able to calculate the projected amount of MSW produced, yet instead I will be doing this will data from recycled waste.f(55)=2.13(55)-19.8 The fifty-five is the years that have passed from 1960 to 2015. This is to show an estimated projection of the amount of MSW that was recycled in the year 2015.f(55)= 117.55-19.8f(55)= 97.4 million tons After plugging it in the function, the output for the x value is 97.4 million tons. This number is the estimated amount of MSW that was actually recycled in the year 2015. The amount of reflected MSW recycled from 2015-2050X (years)Y (amount of MSW recycled in million tons) 2015 (55)97.42020 (60)1082025 (65) 118.62030 (70)129.32035 (75)1402040 (80)150.62045 (85)161.32050 (90)171.9The projected amount of MSW to be recycled was calculated the same way by replacing thexwith the difference in years from 1960 to the projected year. According to the data, the amount of MSW that will be recycled in the U.S. will continue to increase as of 2015 to 2050. These calculations does not take into consideration any fluxuations that could change the data such as an increase in the amount of MSW that could actually be recycled if disposed of properly or if it is made with recyleable material, or an increase in population that can contribute to higher amounts of MSW that cannot be properly recycled. This data is an estimate since it would take a long time to measure the total amount of MSW recycled and these numbers are based off of previous data so it is not entirely accurate. These estimations are good news for the future of this country because it shows that Americans will practice being more enviornmentally friendly which is good news for me since me and my loved ones will have a safe and resourceful country to live in. In order to get a more accurate representation of the data, a graph with a line of best fit is needed which is shown to the right.The graph indicates a steady increase in the amount of MSW estimated to be recycled from 2015 to 2050. Compared to the graph shown for the amount of MSW recycled in 1960 to 2010, the one above is continuously increasing while the one for data from 1960 to 2010 shows more of an exponential growth. There is the possibilities of errors in my projected data causing the graph to look differently, yet I am happy to know that this country will continue to care for the planet. Furthermore, it is important to have a comparison of much MSW was generated by the U.S from 1960-2010 and 2015-2050 and the amount of MSW that was actually recycled from the same time periods to show a comparison of how enviornmentally friendly the U.S. to preserve the lands beauty and to protect it’s people from carniagens. I feel it is also important to know how much MSW is actually polluting the ocean because the waste will not just stay on land but make its way into the home of many marine life forms, some of which we consume. In addition to that, it is very to measure the total amount of surface area the pollution takes up in the ocean because it’s such a vast place and much of the waste is plastic which is detiorated into microscopic pieces.. In order to get a close estimation, my first step is to find how much of the pollution generated by the U.S. is actually spilled into the ocean currently.According to a study done by Jenna Jambeck, an Associate Professor in the College of Engineering at the University of Georgia, the U.S. is responsible for 750,000 lbs of trash found in the ocean as of 2015.  To go from lbs to tons the following steps are:1 lb= 0.0004359237 t In order to go from pounds to tons, it is necessary to multiply.750,000 x0.00045359237=340.2 tons of trash in the ocean With this, it is possible to convert 340.2 tons of trash to determine how many square kilometers the trash takes up in the ocean. According to recent studies, there are approximately 250 billion pieces of trash per Km per every 500 tons of trash in the ocean. This is useful to convert to see how many piece of trash there is in 340.2 tons of trash per square Km. The steps are as followed: 500 tons 340.2 tons= 250 billion piecesxThe first part is to set it up in as a conversion to find x, the number of pieces per square Km per 340.2 tons.500 tons (x) = (250 billion) (340.2 tons) 500 tons (x)= 8.51 x 1013The next step is to cross multiply and leave the answer in scientific notation.x= 8.51 x 1013500x=1.701 x 1011170,100,000,000 billion pieces per square kmAfter simplifying for x, the next step was to put the answer in standard notation. These calculations were done assuming that the MSW was theoretically placed side by side froming a layer a trash on the ocean’s surface. This is not taking into consideration the density of the MSW determining if whether it would sink or not and if some of it was consumed by marine animals.  I did this in order to ensure I am calculating the amount of surface area the MSW takes up in the ocean and not the amount of volume the waste takes up in the ocean.  Now that the number of pieces of trash per square km is found, the next part is to see how much of the ocean’s surface is taken up by trash produced by the U.S. The ocean takes up about 70% of the Earth’s surface; the other 30% is taken up by land.  The initial task will be finding the surface area of the entire earth by using the formula to find the surface area of a sphere:SA=4r2With this equation, I will replace r with the radius of the earth which is between 6,353-6,384 km or 6,371km.SA=46,3712=440,589,641510,064,471.9 sq kmThese calculations are based on the concept of the Earth being a perfect sphere, yet because the Earth is not completely spherical, these calculations are not accurate. Considering the land takes up 148,300,000 sq km, then finding the surface area of the  ocean would take simple subtraction.510,064,471.9-148,300,000=361,764,471.9 km2So, the total surface area of the ocean is361,764,471.9 km2. However, this is calculated disregarding the changing of the topography of the Earth. Finally to find the amount of MSW generated by the U.S. in 2017 covering the ocean can be found by multiplying the surface area of the ocean’s surface by the amount of pieces of trash per square kilometer:361,746,471.9170,100,000,000=6.15 x 1019 pieces of trash As seen in the IA, the amount of MSW being generated by the United States has since increased since the 1960s.  This has been calculated by creating functions that fit the data already calculated to project an estimate on how much MSW will be produced by the U.S. in the future. However, the amount of trash being recycled has since also increased as seen through similar calculations took when calculating the amount of trash, but there that’s not to say that the garbage produced by the U.S. being dumped into the ocean will disappear. In order to keep track of our carbon footprint, it’s best to see the effect humans and their garbage have on the earth, especially the ocean. As calculated, there is estimated to be 6.15 x 1019pieces of trash in the ocean in 2017. I feel like this IA will help open the eyes of others and everyone will be able understand that their impact on this planet today can lead to a chain of events for future generations who will call this country their home. I am glad to know that much of the MSW is recycled which gives me a reason to continue my passion of preserving the Earth and our oceans. It’s important to remember the amount of trash in the ocean can be reduce as long as we all work together to watch how much waste we use and remeber where it all ends up.